# Propagation of Chaos for reflecting diffusions with local-time dependent noise

## TL;DR

This paper establishes the propagation of chaos for systems of reflecting diffusions with local-time dependent noise, linking microscopic stochastic dynamics to macroscopic reaction-diffusion equations.

## Contribution

It introduces a novel analysis of reflecting diffusions with local-time dependent noise and characterizes their hydrodynamic limit through propagation of chaos.

## Key findings

- Existence and uniqueness of the reaction-diffusion equation with non-linear diffusivity.
- Characterization of the large-scale behavior of the system.
- Distribution of hitting times for the reflection local-time.

## Abstract

We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function of the reflection local-time of the system, and by characterizing the large-scale (hydrodynamic) behavior by showing propagation of chaos. In addition, we analyze the one-particle case by computing the distribution of the hitting times of its reflection local-time. This work is the noise analog of work done by Frank Knight (2001).